We show a spin superconductor in ferromagnetic graphene as the counterpart to the charge superconductor in which a spin-polarized electron-hole pair plays the role of the spin 2(/2) ``Cooper pair'' with a neutral charge. We present a BCS-type theory for the spin superconductor. With the ``London-type equations'' of the super-spin-current density, we show the existence of an electric ``Meissner effect'' against a spatial varying electric field. We further study a spin superconductor/normal conductor/spin superconductor junction and predict a spin-current Josephson effect.
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Sun et al. (2011) studied this question.
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